Which breakout board should I use?
Having 2 different boards has lead to a number of people asking which one they should use. Hopefully I can help you work through this question efficiently.
To start off, the main product page has a side by side comparison of the Pico, Teensy and Arduino "Classic" (8-bit ATMega chips). This may help quickly zero in on the important features for you. Take a look at it - I will refer to information from it as we go.
The first thing to consider is how many axes (er, motors) you have. The PicoCNC has 4 axes/motors and the Teensy T41U5XBB has 5. A simple 3 Axis machine with a moving bed will only require 3 motors, one for each axis. If you have the widely common moving gantry machine with a motor on each side of the gantry, you have a 3 Axis machine but need 4 motors. In these two cases, either board will work fine. (well that doesn't help, I'm sure you are thinking...) And both boards support auto-squaring - an important feature that allows you to keep your moving gantry square to the other axis. If you wish to add a rotary axis, you will want the Teensy version. If you have a moving bed machine, you could use the PicoCNC but moving bed + rotary axis is fairly uncommon.
A target use case for PicoCNC is Arduino replacement. If you have a CNC machine using external drivers with an Arduino CNC shield, the PicoCNC is a direct drop in replacement. Given the low cost of the Pico itself, the all-in cost is about $50. That brings you some real benefits over the Arduino - faster step rate (so you can get higher speed), better EMI resistance, more features like auto-squaring.
Another consideration is the EMI environment. Electromagnetic interference can be very frustrating. It is not predictable and often strikes in the middle of job. There are a lot of well understood techniques for hardening your machine to EMI - shielded wiring, solid earth ground, separating signals from EMI sources and so on. In designing the breakout boards we have tried to use good anti-EMI practices. The PicoCNC uses 12V for external input signals: limit/homing sensors, probe, control signals. Using 12V means EMI will have to be a lot more powerful to cause problems. Both board use opto isolators which also helps a lot to keep EMI outside the core electronics. A common channel for EMI is USB. I see many people asking for help with their CNC machine crashing randomly and very often it turns out to be EMI delivered via the USB connection. The absolutely best way to fix this is to use Ethernet to connect. Ethernet uses transformers as part of the connection so it is inherently galvanically isolated and the protocol is error correcting so disruptions will be repaired automatically. The Teensy board supports Ethernet so I highly recommend that for environments that have a lot of EMI. The PicoCNC supports WiFi connectivity (via the Pico W) and, this too, is EMI resilient. It is a good solution for less EMI intensive environments though the WiFi signal can be significantly disrupted. Things like welders and plasma cutters can produce a lot of EMI so I recommend the Teensy with Ethernet over the PicoCNC there but it is a good choice otherwise.
In the area of processing speeds, both boards are good and can feed most commercial stepper and servo drivers at their maximum rate. The Teensy processor is 4.6 times faster than the already fast Pico. The Teensy also has around 7 times more RAM than the Pico. This means that you can do things like increase the look ahead buffer significantly which increases the performance when using a lot of short moves. For a Laser cutter this can be a big benefit. Cost. The Teensy itself is about $30 US dollars, sometimes more depending on the distributor. (If you can, I suggest ordering directly from PJRC.com.) The Pico is typically $4 and the Pico W is $6. The two breakout board with their basic assembly kits are about the same price each so the PicoCNC is a lower cost approach due the cost of the Pico itself. In fact, when you factor in the cost of a CNC shield, the PicoCNC is very cost competitive with an Arduino based solution.
Well, there you have it. Feel free to ask questions, I read and reply.
About the author. Phil Barrett is a long time CNC hobbyist and designer of several breakout boards.